CN114460646B - Reflected wave travel time inversion method based on wave field excitation approximation - Google Patents
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Abstract
The invention belongs to the field of marine seismic exploration, and particularly discloses a reflected wave travel time inversion method based on wave field excitation approximation, which comprises the following steps of: calculating a background wave field by combining the given seismic wavelets and the observation seismic data with an initial velocity model; calculating an accompanying background wave field by taking observed seismic data as a seismic source, and calculating a reverse time migration result; restoring a background wave field and calculating a disturbance wave field; establishing a gradient equation of reflection wave travel time inversion based on a disturbance wave field, calculating a gradient, determining the step size according to the gradient, and obtaining the speed updating amount of the iteration; and iteratively updating the speed parameters until the convergence condition is met, and outputting speed data which is the final inversion result. The method disclosed by the invention only stores the excitation amplitude and the excitation time of the wave field, can improve the inversion efficiency of reflected wave travel, greatly reduces the storage consumption, and provides technical support for the modeling of the background speed of marine seismic exploration.
Description
Technical Field
The invention belongs to the field of marine seismic exploration, and particularly relates to a reflected wave travel time inversion method based on wave field excitation approximation.
Background
Marine seismic inversion estimates corresponding geophysical parameters through observed seismic data, and further reversely deduces the structural morphology and material components of the seabed underground, so that geological structures can be effectively identified, natural disasters can be predicted, and oil and gas reservoirs can be explored. The propagation velocity of the seismic wave is not only the main basis for processing and interpreting seismic data, but also is important data reflecting the structure and lithology of the underlying medium. Therefore, it is important to find the precise velocity of the seismic waves propagating in the ground.
The reflection wave travel time inversion is based on a wave theory, a target function is established by matching travel time information of simulated seismic reflection data and observed seismic reflection data, a local optimization method is used for iteratively searching a global minimum value of the target function, the background speed of seabed sediments can be effectively recovered, an accurate initial speed model can be provided for inversion and imaging technologies such as full waveform inversion and reverse time migration, and the like, and the method is one of the leading edge directions of the current marine seismic exploration field. However, since the inversion algorithm for traveling the reflected waves needs to introduce an offset/inverse offset process to calculate the disturbance wave field, and each iteration process needs to store the data of the background wave field and the disturbance wave field at the same time, huge time consumption is caused by massive storage requirements, and the step of the inversion algorithm for traveling the reflected waves to actual production and application is restricted.
Disclosure of Invention
In order to solve the technical problems, the invention provides a reflected wave travel time inversion method based on wave field excitation approximation so as to achieve the purposes of reducing wave field storage consumption and improving inversion efficiency.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a reflected wave travel time inversion method based on wave field excitation approximation comprises the following steps:
(1) calculating a background wave field by combining the given seismic wavelets and observation seismic data with an initial velocity model, and storing the excitation amplitude and the excitation time of the background wave field;
(2) calculating an accompanying background wave field by using the observed seismic data as a seismic source, and reading the excitation time in the step (1) to calculate a reverse time migration result;
(3) reading the excitation amplitude in the step (1) to recover a background wave field, calculating a disturbance wave field by combining the reverse time migration result in the step (2), and storing the excitation amplitude and the excitation time of the uplink disturbance wave field;
(4) establishing a gradient equation of reflection wave travel time inversion based on a disturbance wave field, calculating a gradient, determining the step size according to the gradient, and obtaining the speed updating amount of the iteration;
(5) and iteratively updating the speed parameters until a convergence condition is met, and outputting speed data which is a final inversion result.
In the scheme, the step (1) is specifically as follows: inputting known observation seismic data, an initial velocity model and a seismic source wavelet, and numerically solving an acoustic wave equation (1) by adopting a staggered grid finite difference method of 2 orders in time and 10 orders in space to obtain a background wave field
And preserving the excitation amplitude of the background wave field
And excitation time
；
Wherein, the first and the second end of the pipe are connected with each other,
which represents the operator of the propagation of the acoustic wave,
representing a source wavelet vector.
In the scheme, the step (2) is specifically as follows: replacing the seismic source wavelet in the acoustic wave equation (1) with observation seismic data, adopting a staggered grid finite difference method of time order 2 and space order 10 to solve the acoustic wave equation (1) numerically, calculating an accompanying background wave field, and obtaining a reverse time migration result based on the excitation time cross-correlation background wave field and the accompanying background wave field in the step (1).
In the scheme, the step (3) is specifically as follows:
reading the excitation amplitude in step (1)
Recovering the background wavefield from equation (2)
：
Wherein the symbol "+" represents a convolution,
representing a source wavelet vector;
adopting a time 2-order and space 10-order staggered grid finite difference method to numerically solve a Born forward equation (3) and calculate a disturbance wave field
Storing the excitation amplitude and the excitation time of the uplink disturbance wave field;
Wherein, the first and the second end of the pipe are connected with each other,
representing a velocity disturbance, where the velocity disturbance is replaced with a reverse time migration result;
calculation of the perturbing wavefield:
wherein, the first and the second end of the pipe are connected with each other,
a propagation operator is represented which is a function of,
a model parameter perturbation operator is represented and is represented,
representing the excitation amplitude of the perturbation wave field.
In the scheme, the step (4) is specifically as follows: and defining an L2 norm target function of inversion during reflected wave travel, obtaining a gradient equation based on wave field excitation approximation according to the target function, and giving a proper step length to obtain the speed updating quantity of the iteration.
In a further technical scheme, an L2 norm objective function of inversion when a reflected wave travels is defined:
wherein, the first and the second end of the pipe are connected with each other,
the function of the object is represented by,
a parameter representing the speed of the background is shown,
representing travel time differences of observed seismic data and simulated seismic data,
is shown and
the norm of the L2 in question,
calculated from cross-correlation auxiliary equation (6):
wherein the content of the first and second substances,
and
respectively representing observed seismic data and simulated seismic data at the position of the detection point, and simulating seismic data
From a perturbing wave field
，
Represents time; when the cross-correlation value of equation (6) reaches the maximum, the corresponding one
Is equal to
；
According to equations (5) and (6), a gradient equation for inversion at the time of travel of the reflected wave is derived based on the adjoint state method, and equations (2) and (4) are substituted into the gradient equation to obtain equation (7):
Wherein, the first and the second end of the pipe are connected with each other,
which is indicative of the gradient of the light beam,
which represents the inner product operation of two vectors,
and
representing the second time derivatives of the background and perturbation wave fields respectively,
and
respectively representing the adjoint background wavefield and the adjoint disturbance wavefield,
representing the second time derivative of the source wavelet vector,
represents zero lag cross-correlation; the adjoint background wavefield and the adjoint disturbance wavefield are computed by solving equations (1) and (3), respectively, where the source wavelet vector is
Accompanying seismic source replaced by reflected wave travel time inversion method
See equation (8);
and (5) according to equation (7), giving a proper step length to obtain the speed updating amount of the iteration.
In the scheme, in the step (5), the speed updating amount of each iteration is ensured to be between 20m/s and 100m/s, and the speed parameter is updated iteratively until the convergence condition is met.
In a further technical scheme, the convergence condition is as follows: and (3) calculating a square value of an error when the iterative simulated seismic data and the observed seismic data travel at the time, comparing the square value with a value of the last iteration, if the numerical value is reduced, continuing to perform the step (1), and when the square value of the error is continuously in a non-descending state for 5 times, determining that the inversion method has converged to a global minimum value to meet a convergence condition, wherein at the moment, the output speed data is a final inversion result.
Through the technical scheme, the reflection wave travel time inversion method based on wave field excitation approximation has the following beneficial effects:
the method carries out excitation approximation on the background wave field and the disturbance wave field in the reflected wave travel time inversion method, only stores the excitation amplitude and the excitation time, avoids storage and read-write operation of a full wave field, and can effectively reduce storage consumption of reflected wave travel time inversion. In addition, the convolution of the excitation amplitude and the seismic source vector can effectively avoid the problem of wave field seismic source feature loss, the integrity of the waveform is ensured, the storage of the uplink wave excitation amplitude solves the problem of wave path of a disturbance wave field, and the precision of the reflected wave travel time inversion method based on wave field excitation approximation is improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments or the prior art descriptions will be briefly described below.
FIG. 1 is a schematic flow chart of an embodiment of a reflection wave travel-time inversion method based on wave field excitation approximation disclosed in the present invention;
FIGS. 2a-2b are Sigsbee2A velocity models, where FIG. 2a is the true velocity model; FIG. 2b is an initial velocity model;
3a-3b are contrasts of conventional reflected wave traveltime inversion gradients with the present invention wavefield excitation based approximation of reflected wave traveltime inversion gradients, where FIG. 3a is the gradient of the conventional reflected wave traveltime inversion; FIG. 3b is the gradient of the reflection travel-time inversion of the wavefield excitation approximation according to the present invention;
4a-4b are results of conventional reflection travel time inversion, where FIG. 4a is the longitudinal velocity inverted after 40 iterations; FIG. 4b is a RTM result corresponding to the inverse longitudinal wave velocity;
FIGS. 5a-5b are the results of the reflection travel-time inversion of the wavefield excitation approximation according to the present invention, where FIG. 5a is the longitudinal wave velocity inverted after 40 iterations; fig. 5b shows RTM results corresponding to the inverse longitudinal wave velocity.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention.
The invention provides a reflected wave travel time inversion method based on wave field excitation approximation, as shown in figure 1, a specific technical scheme is explained through model testing:
(1) calculating a background wave field by combining the given seismic wavelets and observation seismic data with an initial velocity model, and storing the excitation amplitude and the excitation time of the background wave field;
The method comprises the following specific steps:
inputting known observation seismic data, an initial velocity model and a seismic source wavelet, and numerically solving an acoustic wave equation (1) by adopting a staggered grid finite difference method of 2 orders in time and 10 orders in space to obtain a background wave field
And preserving the excitation amplitude of the background wave field
And excitation time
；
Wherein, the first and the second end of the pipe are connected with each other,
which represents the operator of the propagation of the acoustic wave,
representing a source wavelet vector.
The seismic wavelets during model test are generally given to Rake wavelets, and the seismic wavelets during actual application are generally obtained by a wavelet inversion technology; observing seismic data, mainly referring to seismic data of vertical components received by a surface geophone; the velocity value of the initial velocity in the initial velocity model generally increases gradually from the shallow layer to the deep layer.
(2) Taking the observed seismic data as a seismic source, calculating an accompanying background wave field, and reading the excitation time in the step (1) to calculate a reverse time migration result;
the method comprises the following specific steps: replacing the source wavelet in the acoustic wave equation (1) with the observation seismic data, numerically solving the acoustic wave equation (1) by adopting a staggered grid finite difference method of 2 orders in time and 10 orders in space, calculating an accompanying background wave field, and obtaining a reverse time migration result based on the excitation time cross-correlation background wave field and the accompanying background wave field in the step (1).
(3) Reading the excitation amplitude in the step (1) to recover a background wave field, calculating a disturbance wave field by combining the reverse time migration result in the step (2), and storing the excitation amplitude and the excitation time of the uplink disturbance wave field;
the method comprises the following specific steps:
reading the excitation amplitude in step (1)
Recovery of the background wavefield from equation (2)
：
Wherein the symbol "+" indicates a convolution,
representing a source wavelet vector; the wavefield after the approximation is excited loses the seismic source characteristics, and the excitation amplitude convolution seismic source signal vector is used for recovering the background wavefield.
Adopting a time 2 order and space 10 order staggered grid finite difference method to numerically solve a Born forward equation (3) and calculate a disturbance wave field
Storing the excitation amplitude and the excitation time of the uplink disturbance wave field;
wherein, the first and the second end of the pipe are connected with each other,
representing a velocity disturbance, where the velocity disturbance is replaced with a reverse time migration result;
calculation of the perturbing wavefield:
wherein the content of the first and second substances,
the propagation operator is represented by a number of propagation operators,
representing a perturbation operator of the model parameters,
representing the excitation amplitude of the perturbation wave field.
The seismic source characteristics of the disturbance wave field can be recovered by convolution of the seismic source signal vector by the excitation amplitude of the disturbance wave field, and the excitation amplitude of the uplink disturbance wave field is saved
For solving the problem of multipath of the perturbing wavefield.
(4) Establishing a gradient equation of reflection wave travel time inversion based on a disturbance wave field, calculating a gradient, determining the step size according to the gradient, and obtaining the speed updating amount of the iteration;
the method comprises the following specific steps: and defining an L2 norm target function of inversion when the reflected wave travels, obtaining a gradient equation based on wave field excitation approximation according to the target function, and giving a proper step length to obtain the speed updating amount of the iteration.
Defining an L2 norm objective function for the reflection travel time inversion:
wherein, the first and the second end of the pipe are connected with each other,
the function of the object is represented by,
a parameter representing the speed of the background is indicated,
representing travel time differences of observed seismic data and simulated seismic data,
is shown and
the norm of the L2 in question,
calculated from cross-correlation auxiliary equation (6):
wherein the content of the first and second substances,
and
respectively representing observed seismic data and simulated seismic data at the position of the detection point, and simulating seismic data
From a perturbing wave field
，
Represents time; when the cross-correlation value of equation (6) reaches the maximum, the corresponding one
Is equal to
；
According to equations (5) and (6), a gradient equation for inversion at the time of travel of the reflected wave is derived based on the adjoint state method, and equations (2) and (4) are substituted into the gradient equation to obtain equation (7):
wherein the content of the first and second substances,
the gradient is represented by the number of lines,
representing the inner product operation of two vectors, 
And
representing the second time derivatives of the background and perturbation wave fields respectively,
and
respectively representing the adjoint background wavefield and the adjoint disturbance wavefield,
representing the second time derivative of the source wavelet vector,
represents zero lag cross-correlation; the adjoint background wavefield and the adjoint disturbance wavefield are calculated by solving equations (1) and (3), respectively, wherein the source wavelet vector
Adjoint seismic source replaced by reflected wave travel time inversion method
See equation (8);
according to equation (7), only the excitation amplitude of the background wavefield needs to be stored for each gradient calculation
And excitation amplitude of up-going disturbance wavefield
And the corresponding excitation time, avoids the storage of the entire background wavefield and the disturbance wavefield. And (5) according to equation (7), giving a proper step length to obtain the speed updating amount of the iteration.
Fig. 2-5 perform numerical tests of reflection travel-time inversion based on wavefield excitation approximation with a sigabe 2A model, where fig. 2a and 2b show the initial velocity and true velocity of the sigabe 2A model. Fig. 3a and 3b show the gradient results of conventional reflection travel-time inversion and reflection travel-time inversion based on wavefield excitation approximation, respectively, with a slight difference in energy, mainly because the wavefields inverted during conventional reflection travel are multipath. The calculation requirements for the single shot gradient are shown in table 1.
TABLE 1 comparison of computational storage requirements for single shot gradients
| Method | Wave field dimension | Memory space | Time |
| Conventional methods | 351*184*2000 | 985.47MB | 57.87s |
| Excitation approximation | 351*184 | 0.99MB | 47.13s |
The conventional reflection travel-time inverse gradient requires storing four wavefields
The dimension of a single wavefield is 351 x 184 x 2000, and since the wavefield file can be reused, only two wavefield files need to be saved, and the storage capacity for the conventional reflection wave traveling inversion is 985.47 MB. The excitation amplitude and the excitation time need to be saved in the excitation approximate reflection wave traveling inversion algorithm, and four files need to be saved finally because the files can be reused, the storage capacity of the files is 0.99MB, and the storage capacity is reduced by nearly 1000 times, which is mainly related to the number of time sampling points.
(5) And iteratively updating the speed parameters until a convergence condition is met, and outputting speed data which is a final inversion result.
And determining the step size according to the gradient, ensuring that the speed updating amount of each iteration is between 20m/s and 100m/s, and iteratively updating the speed parameter until a convergence condition is met.
The convergence conditions are as follows: and (3) calculating a square value of an error when the iterative simulated seismic data and the observed seismic data travel at the time, comparing the square value with a value of the last iteration, if the numerical value is reduced, continuing to perform the step (1), and when the square value of the error is continuously in a non-descending state for 5 times, determining that the inversion method has converged to a global minimum value to meet a convergence condition, wherein at the moment, the output speed data is a final inversion result.
After 40 iterations, the longitudinal wave velocity recovered by the conventional reflection wave travel time inversion is shown in fig. 4a, and fig. 4b is the reflection wave travel time inversion result corresponding to fig. 4 a. Similarly, after 40 iterations, the longitudinal wave velocity of the excitation approximate reflection wave travel time inversion recovery is shown in fig. 5a, and it can be seen that the excitation approximate reflection wave travel time inversion mainly updates low wave number components in a velocity model, the precision of the excitation approximate reflection wave travel time inversion is almost not different from that of the conventional reflection wave travel time inversion, the longitudinal wave velocity shown in fig. 5a is used as an initial model, an inverse time migration result is obtained and is shown in fig. 5b, an imaging result is focused, no arc drawing phenomenon occurs on a diffraction body at a middle-deep layer position, and the diffraction body obtains good migration homing, which shows that the excitation approximate reflection wave travel time inversion can provide an accurate longitudinal wave velocity model of the low wave number components.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (8)
1. A reflected wave travel time inversion method based on wave field excitation approximation is characterized by comprising the following steps:
(1) calculating a background wave field by combining the given seismic wavelets and observation seismic data with an initial velocity model, and storing the excitation amplitude and the excitation time of the background wave field;
(2) calculating an accompanying background wave field by using the observed seismic data as a seismic source, and reading the excitation time in the step (1) to calculate a reverse time migration result;
(3) reading the excitation amplitude in the step (1) to recover a background wave field, calculating a disturbance wave field by combining the reverse time migration result in the step (2), and storing the excitation amplitude and the excitation time of the uplink disturbance wave field;
(4) establishing a gradient equation of reflection wave travel time inversion based on a disturbance wave field, calculating a gradient, determining the step size according to the gradient, and obtaining the speed updating amount of the iteration;
(5) and iteratively updating the speed parameters until a convergence condition is met, and outputting speed data which is a final inversion result.
2. The method for reflection wave travel-time inversion based on wavefield excitation approximation as claimed in claim 1, wherein the step (1) is as follows: inputting known observation seismic data, an initial velocity model and a seismic source wavelet, and numerically solving an acoustic wave equation (1) by adopting a staggered grid finite difference method of 2 orders in time and 10 orders in space to obtain a background wave field 
And preserving the excitation amplitude of the background wave field
And excitation time
；
Wherein, the first and the second end of the pipe are connected with each other,
which represents the operator of the propagation of the acoustic wave,
representing a source wavelet vector.
3. The method for reflection wave travel-time inversion based on wavefield excitation approximation as claimed in claim 2, wherein the step (2) is specifically as follows: replacing the seismic source wavelet in the acoustic wave equation (1) with observation seismic data, adopting a staggered grid finite difference method of time order 2 and space order 10 to solve the acoustic wave equation (1) numerically, calculating an accompanying background wave field, and obtaining a reverse time migration result based on the excitation time cross-correlation background wave field and the accompanying background wave field in the step (1).
4. The method for reflection wave travel-time inversion based on wavefield excitation approximation as claimed in claim 2, wherein the step (3) is specifically as follows:
reading the excitation amplitude in step (1)
Recovering the background wavefield from equation (2)
：
Wherein the symbol "+" represents a convolution,
representing a source wavelet vector;
adopting a time 2-order and space 10-order staggered grid finite difference method to numerically solve a Born forward equation (3) and calculate a disturbance wave field
Storing the excitation amplitude and the excitation time of the uplink disturbance wave field;
Wherein, the first and the second end of the pipe are connected with each other,
representing a model parameter disturbance operator, wherein the speed disturbance is replaced by a reverse time migration result;
calculation of the perturbing wavefield:
wherein, the first and the second end of the pipe are connected with each other,
representing the excitation amplitude of the perturbation wave field.
5. The method for reflection wave travel-time inversion based on wavefield excitation approximation as claimed in claim 4, wherein the step (4) is as follows: and defining an L2 norm target function of inversion during reflected wave travel, obtaining a gradient equation based on wave field excitation approximation according to the target function, and giving a proper step length to obtain the speed updating quantity of the iteration.
6. The method of claim 5, wherein an L2 norm objective function for the reflection travel time inversion is defined:
wherein, the first and the second end of the pipe are connected with each other,
the function of the object is represented by,
a parameter representing the speed of the background is indicated,
representing travel time differences of observed seismic data and simulated seismic data,
is shown and
the norm of the L2 in question,
calculated from cross-correlation auxiliary equation (6):
wherein the content of the first and second substances,
and
respectively representing observed seismic data and simulated seismic data at the position of the detection point, and simulating seismic data
From a perturbing wave field
，
Represents time; when the cross-correlation value of equation (6) reaches the maximum, the corresponding one 
Is equal to
；
Deriving a gradient equation for reflection wave travel-time inversion based on the adjoint state method according to equations (5) and (6), and substituting equations (2) and (4) into the gradient equation to obtain equation (7):
wherein, the first and the second end of the pipe are connected with each other,
which is indicative of the gradient of the light beam,
which represents the inner product operation of two vectors,
and
representing the second time derivatives of the background and perturbation wave fields respectively,
and
respectively representing the adjoint background wavefield and the adjoint disturbance wavefield,
representing the second time derivative of the source wavelet vector,
indicating a zero-lag cross-correlation,
representing an excitation amplitude of the upgoing disturbance wavefield; the adjoint background wavefield and the adjoint disturbance wavefield are calculated by solving equations (1) and (3), respectively, wherein the source wavelet vector
Adjoint seismic source replaced by reflected wave travel time inversion method
See equation (8);
and (5) according to equation (7), giving a proper step length to obtain the speed updating amount of the iteration.
7. The method for reflection wave travel-time inversion based on wave field excitation approximation as claimed in claim 1, wherein in step (5), the velocity parameter is iteratively updated until the convergence condition is satisfied while ensuring that the velocity update amount of each iteration is between 20m/s and 100 m/s.
8. The method of claim 7, wherein the convergence condition is: and (3) calculating a square value of an error when the iterative simulated seismic data and the observed seismic data travel at the time, comparing the square value with a value of the last iteration, if the numerical value is reduced, continuing to perform the step (1), and when the square value of the error is continuously in a non-descending state for 5 times, determining that the inversion method has converged to a global minimum value to meet a convergence condition, wherein at the moment, the output speed data is a final inversion result.
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